Linear Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Functional Analysis write by Bryan Rynne. This book was released on 2013-03-14. Linear Functional Analysis available in PDF, EPUB and Kindle. This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
Linear Functional Analysis
Linear Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Functional Analysis write by Hans Wilhelm Alt. This book was released on 2016-07-06. Linear Functional Analysis available in PDF, EPUB and Kindle. This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.
Linear Functional Analysis
Linear Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Functional Analysis write by Joan Cerda. This book was released on 2010. Linear Functional Analysis available in PDF, EPUB and Kindle. Presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. It avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems. The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology.
Linear Functional Analysis
Linear Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Functional Analysis write by Bryan P. Rynne. This book was released on 2000. Linear Functional Analysis available in PDF, EPUB and Kindle. This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book.
Linear and Nonlinear Functional Analysis with Applications
Linear and Nonlinear Functional Analysis with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Nonlinear Functional Analysis with Applications write by Philippe G. Ciarlet. This book was released on 2013-10-10. Linear and Nonlinear Functional Analysis with Applications available in PDF, EPUB and Kindle. This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.
